4t=8.5(t-1/2)

Solution for 4t=8.5(t-1/2) equation:

4t=8.5(t-1/2)

We move all terms to the left:

4t-(8.5(t-1/2))=0

We add all the numbers together, and all the variables

4t-(8.5(+t-1/2))=0

We multiply all the terms by the denominator


4t*2))-(8.5(+t-1=0

We add all the numbers together, and all the variables

t+4t*2))-(8.5(-1=0

Wy multiply elements

8t^2+t-1=0

a = 8; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·8·(-1)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{33}}{2*8}=\frac{-1-\sqrt{33}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*8}=\frac{-1+\sqrt{33}}{16}
$